Abstract
We explore the low-energy dynamics of 1/2-BPS heavy particles coupled to the ABJM model via the Higgsing of M2-branes, with focus on physical understanding of the recently discovered 1/2-BPS Wilson loop operators. The low-energy theory of 1/2-BPS heavy particles turns out to have the U(N|N) supergauge symmetry, which explains the novel structure of the 1/2-BPS Wilson loop operator as a holonomy of a U(N|N) superconnection. We show that the supersymmetric transformation of the Wilson loop operator can be identified as a fermionic supergauge transformation, which leads to their invariance under half of the supersymmetry. We also argue that 1/2-BPS Wilson loop operators appear as 1/2-BPS vortices with vorticity 1/k. Such a vortex can be naturally interpreted as a membrane wrapping the \( {\mathbb{Z}_t} \) cycle once, or type IIA fundamental string.
Similar content being viewed by others
References
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, \( \mathcal{N} = 6 \) superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [SPIRES].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [SPIRES].
N. Drukker, J. Plefka and D. Young, Wilson loops in 3-dimensional \( \mathcal{N} = 6 \) supersymmetric Chern-Simons Theory and their string theory duals, JHEP 11 (2008) 019 [arXiv:0809.2787] [SPIRES].
B. Chen and J.-B. Wu, Supersymmetric Wilson Loops in \( \mathcal{N} = 6 \) Super Chern-Simons- matter theory, Nucl. Phys. B 825 (2010) 38 [arXiv:0809.2863] [SPIRES].
S.-J. Rey, T. Suyama and S. Yamaguchi, Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual, JHEP 03 (2009) 127 [arXiv:0809.3786] [SPIRES].
N. Drukker, J. Gomis and D. Young, Vortex Loop Operators, M2-branes and Holography, JHEP 03 (2009) 004 [arXiv:0810.4344] [SPIRES].
N. Drukker and D. Trancanelli, A supermatrix model for \( \mathcal{N} = 6 \) super Chern-Simons-matter theory, JHEP 02 (2010) 058 [arXiv:0912.3006] [SPIRES].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, arXiv:0712.2824 [SPIRES].
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [SPIRES].
T. Suyama, On Large-N Solution of ABJM Theory, Nucl. Phys. B 834 (2010) 50 [arXiv:0912.1084] [SPIRES].
M. Mariño and P. Putrov, Exact Results in ABJM Theory from Topological Strings, JHEP 06 (2010) 011 [arXiv:0912.3074] [SPIRES].
K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [SPIRES].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [SPIRES].
D. Berenstein and D. Trancanelli, Three-dimensional \( \mathcal{N} = 6 \) SCFT’s and their membrane dynamics, Phys. Rev. D 78 (2008) 106009 [arXiv:0808.2503] [SPIRES].
Y. Nakayama, M. Sakaguchi and K. Yoshida, Non-Relativistic M2-brane Gauge Theory and New Superconformal Algebra, JHEP 04 (2009) 096 [arXiv:0902.2204] [SPIRES].
K.-M. Lee, S. Lee and S. Lee, Nonrelativistic Superconformal M2-Brane Theory, JHEP 09 (2009) 030 [arXiv:0902.3857] [SPIRES].
S. Mukhi and C. Papageorgakis, M2 to D2, JHEP 05 (2008) 085 [arXiv:0803.3218] [SPIRES].
E. Koh, S. Lee and S. Lee, Topological Chern-Simons σ-model, JHEP 09 (2009) 122 [arXiv:0907.1641] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1006.5589
Rights and permissions
About this article
Cite this article
Lee, KM., Lee, S. 1/2-BPS Wilson loops and vortices in ABJM model. J. High Energ. Phys. 2010, 4 (2010). https://doi.org/10.1007/JHEP09(2010)004
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2010)004